With the rapid increase of vehicle ownership and stricter environmental regulations, hybrid electric buses have become a focus of research and industrial development. From the perspectives of overall vehicle efficiency, driving performance, and driving range, the parallel hybrid electric bus is considered more suitable for urban driving conditions than series or power-split configurations. This paper addresses the systematic parameter matching and optimization of a parallel hybrid bus powertrain. A complete engineering-oriented design flow is developed, from structure selection and component sizing to control strategy evaluation and cost-based optimization. The proposed methodology provides a theoretical basis for selecting and procuring every powertrain unit in a hybrid bus development project. In addition, the role of the high-voltage battery is highlighted in terms of energy storage, transient power buffering, and fuel economy impact. Extensive simulations using the ADVISOR environment are presented, and the results confirm that the proposed matching procedure can achieve the design targets with an optimal trade-off between fuel economy improvement and system cost.
1. Introduction and Motivation
The global automotive industry is under increasing pressure to reduce petroleum consumption and harmful emissions. Conventional urban buses, which frequently operate under idle, start-stop, acceleration and braking cycles, suffer from poor engine efficiency and high pollutant emission levels. Hybrid electric vehicles (HEVs) combine an internal combustion engine with an electric motor and an energy storage system. The electrical path allows the engine to operate in more efficient regions and enables regenerative braking, yielding substantial fuel savings and emission reductions in urban environments. Among all HEV topologies, the parallel configuration is particularly attractive for city buses because it requires lower electric machine power and a smaller high-voltage battery compared with series hybrids, while still allowing the engine to be downsized and the motor to assist during peak torque demands. The design of such a system involves many coupled parameters, including engine power, motor power, battery pack capacity, transmission ratios, and control thresholds. An improper matching may lead to poor component efficiency, inability to meet acceleration or gradeability targets, or excessive cost. Therefore, this paper develops a complete parameter matching and optimization framework for a 12-meter parallel hybrid city bus.
2. Vehicle Parameters and Performance Targets
Vehicle dynamic fundamentals provide the basis for powertrain design. The tractive force at the driven wheels is expressed as:
$$
F_t = \frac{T_{tq} i_g i_0 \eta_T}{r}
$$
where \(T_{tq}\) is the torque generated by the engine or electric motor, \(i_g\) is the gearbox ratio, \(i_0\) is the final drive ratio, \(\eta_T\) is the driveline efficiency, and \(r\) is the wheel rolling radius. The driving resistance is composed of rolling resistance, aerodynamic drag, gradient resistance, and acceleration resistance:
$$
\sum F = F_f + F_w + F_i + F_j
$$
$$
F_f = W f
$$
$$
F_w = \frac{C_D A u_a^2}{21.15}
$$
$$
F_i = G \sin\alpha \approx G i
$$
$$
F_j = \delta m \frac{du}{dt}
$$
where \(C_D\) is the aerodynamic drag coefficient, \(A\) is the frontal area, \(u_a\) is the vehicle speed, \(\delta\) is the rotational inertia conversion factor, and \(m\) is the vehicle mass.
The urban bus studied in this work has dimensions of \(12000 \times 2550 \times 3250\) mm. The curb weight is 12000 kg, while the gross vehicle weight is 18000 kg. The air-conditioning system and auxiliary loads can consume up to 15 kW. The target fuel economy improvement relative to a conventional diesel bus is 20%. The dynamic performance requirements are listed in Table 1. These targets must be achieved simultaneously with low emissions and acceptable cost.
| Parameter | Value |
|---|---|
| Overall length | 12000 mm |
| Overall width | 2550 mm |
| Overall height | 3250 mm |
| Frontal area \(A\) | 7.2 m² |
| Aerodynamic drag coefficient \(C_D\) | 0.75 |
| Curb mass | 12000 kg |
| Gross vehicle mass | 18000 kg |
| Rolling resistance coefficient | \(0.010+0.0001 u_a\) |
| Rotational mass conversion factor \(\delta\) | 1.1 |
| Wheel rolling radius | 0.52 m |
| Maximum speed | 80 km/h |
| Engine-alone maximum speed | > 65 km/h |
| Gradeability at 50 km/h | > 4% |
| Acceleration time 0–50 km/h | < 25 s |
| Maximum auxiliary load | 15 kW |
Table 1. Main vehicle parameters and design performance targets
3. Driving Cycle Analysis
Urban bus operating statistics show that during typical city routes, the acceleration phase accounts for about 30%, idle duration for about 30%, cruise for less than 20%, and deceleration/braking for about 20% of the total operation time. Such frequent start-stop patterns penalize a conventional drivetrain because the engine consumes fuel during idling and operates at low load during partial urban speed. The ECE driving cycle, shown in Table 2, has been selected in this study for several reasons: it is the standard cycle established for Chinese bus fuel consumption testing, it represents dense urban stop-and-go operations, and it permits direct comparison with published results in the literature. The cycle has a duration of 195 s, a length of 0.99 km, a maximum speed of 50 km/h, a mean speed of 18.26 km/h, and a maximum acceleration of 1.06 m/s².
| Cycle | Duration (s) | Distance (km) | Max speed (km/h) | Average speed (km/h) | Max accel. (m/s²) |
|---|---|---|---|---|---|
| ECE | 195 | 0.99 | 50 | 18.26 | 1.06 |
| CYC_1015 | 660 | 4.16 | 69.97 | 22.68 | 0.79 |
| CBD14 | 569 | 3.23 | 32.19 | 20.43 | 0.98 |
| NYCC | 598 | 1.90 | 44.58 | 11.41 | 2.68 |
Table 2. Representative urban driving cycles
The repeated ECE cycle (30 repetitions) has been used for all simulations in this paper because it allows the charge-sustaining behavior of the high-voltage battery to be observed over a sufficiently long time span while keeping the computation time reasonable.
4. Hybrid Powertrain Architecture Selection
Three main hybrid architectures were considered: series, parallel, and series-parallel. The series architecture requires a large generator, a large traction motor, and abundant battery capacity because the engine is not mechanically connected to the wheels; all engine power must be converted into electricity and then back into mechanical power. This double conversion significantly lowers the total efficiency. The series-parallel architecture offers higher efficiency potential but requires a complex power-split device, a more sophisticated controller, higher cost, and more installation space. For a 12-meter city bus, the parallel architecture is preferred because it can be built with moderate modifications to the conventional chassis, requires a relatively small motor and high-voltage battery pack, and benefits from the established production infrastructure of mechanical transmissions.
Parallel hybrids can be implemented with torque coupling, speed coupling, or wheel coupling. Torque coupling is the most widely used and mature solution for hybrid buses. Two basic torque-coupling configurations exist: single-shaft and dual-shaft. In the single-shaft configuration, the engine and motor are mechanically coupled on the same shaft before the gearbox. If the motor is placed before the gearbox, the gearbox multiplies the output torque of both the engine and the motor, which allows both the engine and motor to be downsized significantly. Such a front-mounted single-shaft architecture has been selected in this project. The system diagram is composed of an electronically controlled diesel engine, a permanent magnet synchronous motor, an automated mechanical transmission (AMT), a clutch between the engine and the motor, a traction battery pack, and the corresponding controllers. The motor controller regulates the bidirectional power flow between the high-voltage battery and the motor, enabling both motoring and regenerative braking.
5. Component Selection and Sizing
5.1 Engine Selection
For parallel hybrid buses, the engine should be sized to supply the average power demand rather than the peak power demand. The engine chosen for this hybrid system is a modern high-speed diesel engine with electronic control. Diesel engines provide higher thermal efficiency, better durability, and lower fuel consumption compared with gasoline engines for heavy-duty applications. The engine maximum power was initially derived from the constant-speed power demand at the target maximum vehicle speed.
$$
P_{tot} = \frac{1}{\eta_T} \left( \frac{Gf}{3600} v_{max} + \frac{C_D A}{76140} v_{max}^3 \right)
$$
Using the vehicle parameters from Table 1 and setting the maximum speed to 80 km/h, the total power at the wheels becomes approximately 132 kW. Adding an air-conditioning load of 15 kW and a power reserve of 12%, the total installed driving power is about 200 kW. This value is consistent with the engine power ratings of conventional 12-meter buses, which range from 162 to 221 kW. In this paper, the total powertrain power is fixed at 200 kW for the evaluation of different hybrid degrees.
The minimum engine power is determined by the engine-alone maximum speed of 65 km/h. The corresponding demand is calculated as:
$$
P_{e,min} \ge \frac{1}{\eta_T} \left( \frac{Gf}{3600} v_{e,max} + \frac{C_D A}{76140} v_{e,max}^3 \right)
$$
This gives approximately 89 kW. With a 12% margin, the minimum engine output becomes 100 kW. In the subsequent optimization, the engine power is varied according to the chosen hybrid degree, but the total sum of the engine power and the motor power remains 200 kW.
5.2 Motor Selection
The motor in a parallel hybrid bus acts as a torque booster during acceleration and hill climbing, and as a generator during braking and engine-charging modes. The motor must be capable of bidirectional operation and high-efficiency operation over a broad speed range. Permanent magnet synchronous motors (PMSM) are selected because they have high power density, high efficiency (up to 95%), low rotor losses, and excellent controllability. The motor base speed is chosen around 1500 rpm to match the efficient speed region of the diesel engine used in the bus. When the motor is placed before the gearbox, the required motor torque is reduced by the gearbox ratio, so a peak torque of at least 400 N·m is needed from studies of the maximum gradient requirement:
$$
T_{m,max} \ge \frac{mg (f \cos\alpha_{max} + \sin\alpha_{max}) r}{i_{g1} i_0 \eta_T}
$$
where \(i_{g1}\) is the first-gear ratio. With the chosen transmission, the required motor torque becomes about 400 N·m. Therefore, the minimum continuous motor power is 40 kW. The actual motor power is selected as \(P_m = R \times P_{tot}\), where \(R\) is the hybrid degree.
5.3 Energy Storage System and the Role of the High-Voltage Battery
The energy storage device is one of the most critical components in a hybrid bus. It must supply peak power during motor-assist operation, absorb regenerative braking energy, and maintain high round-trip efficiency. Among various options, lead-acid batteries have low energy and power density plus a short cycle life, and they also cause environmental concerns. Nickel-metal hydride batteries have been commercially successful but their performance potential is nearly exhausted. Supercapacitors have very high cycle life and efficiency but low energy density and high specific cost. Lithium-ion chemistry offers the best overall balance for hybrid buses: high specific energy (75–120 Wh/kg), high specific power (1000–1300 W/kg), high coulombic efficiency (about 90%), and reasonable cost projections. The integration of a lithium-ion high-voltage battery is therefore chosen for this design. The high-voltage battery pack must be managed by a battery management system (BMS) that monitors cell voltage, current, temperature, and state of charge (SOC). The BMS also keeps SOC within a favorable window, typically between 50% and 85%, to reduce internal resistance and prolong life. Table 3 compares the main energy storage technologies.
| Item | Li-ion battery | NiMH battery | Supercapacitor | Lead-acid battery |
|---|---|---|---|---|
| Energy density (Wh/kg) | 75–120 | 50–70 | 3–4 | 20–30 |
| Power density (W/kg) | 1000–1300 | 1000–1500 | 1000–3000 | 200–500 |
| Energy cost (USD/kWh) | 1000–2000 | 1000 | 15000 | 100–200 |
| Power cost (USD/kW) | 60–120 | 40–70 | 15–25 | 5–20 |
| Cycle efficiency (%) | 90 | 75 | 95 | 75 |
| Life (cycles) | 1000–3000 | 2000 | 500000–1000000 | 300–600 |
| Temperature range (°C) | -20 to 60 | -10 to 50 | -40 to 65 | -20 to 70 |
Table 3. Comparison of energy storage systems
In the simulation model, the high-voltage battery is represented as a controlled voltage source in series with an internal resistance. The terminal voltage during discharge is
$$
U_{bd} = E_{bat} – I_{bd} R_{bd}
$$
and during charge,
$$
U_{bc} = E_{bat} – I_{bc} R_{bc}
$$
where \(E_{bat}\) is the open-circuit voltage and \(R_{bd}\) and \(R_{bc}\) denote the discharge and charge internal resistance, respectively. These values are functions of SOC and temperature. The SOC is calculated by Coulomb counting with load-based correction:
$$
SOC = SOC_0 – \frac{1}{C} \int I(t)\,dt
$$
The nominal pack voltage in this work is selected to be compatible with the motor controller and is designated as a high-voltage battery system of 336 V class. The pack capacity is sized such that the C-rate remains within acceptable limits during both acceleration and regenerative braking events.
5.4 Transmission and Final Drive
An automated mechanical transmission (AMT) is selected over a conventional manual transmission (MT), automatic transmission (AT), and continuously variable transmission (CVT). The CVT power limitation prohibits its use in heavy-duty buses. ATs suffer from torque converter losses during launch and low-speed operation, which lowers fuel economy and reduces the amount of regenerative energy recovered through the drivetrain. MTs are difficult to coordinate with the hybrid controller because clutch and shift actions rely on driver skills and can cause safety hazards during electric-only braking. An AMT, on the other hand, allows the entire hybrid control unit to manage clutch, gear shifting, motor speed synchronization, and engine throttling in a coordinated manner. The proposed AMT has six forward ratios: 6.98, 4.06, 2.74, 1.89, 1.31, and 1.0. The final drive ratio is chosen as \(i_0 = 6.5\), which satisfies both the maximum vehicle speed and motor high-efficiency operation.
The maximum speed condition requires:
$$
i_0 \le \frac{0.377 n_{max} r}{v_{max}}
$$
which gives \(i_0 \le 6.98\), assuming an engine speed limit of 2850 rpm. In addition, the motor should still be able to deliver full power near the maximum vehicle speed:
$$
i_0 \ge \frac{0.377 n_{ep} r}{v_{max}}
$$
Using \(n_{ep} = 2500\) rpm gives \(i_0 \ge 6.13\). Therefore \(i_0 = 6.5\) is a suitable compromise.
6. Operating Modes and Control Strategy
The parallel hybrid bus has several operating modes according to the torque demand and SOC status:
| Mode | Condition | Engine | Motor | Description |
|---|---|---|---|---|
| Pure electric | Low load, high SOC | Off | Drive | Motor alone drives the bus at start-up or light cruise |
| Engine only | Medium load, SOC normal | On | Idle/Off | Engine meets the traction requirement |
| Hybrid drive | High load, high SOC | On | Assist | Motor adds torque to the engine output |
| Charge sustaining | Low SOC, medium load | On | Generating | Engine produces extra torque to charge the high-voltage battery |
| Regenerative braking | Braking or deceleration | Off | Generating | Motor recovers kinetic energy and charges the battery |
| Idle stop | Vehicle stopped | Off | Off | Engine is shut down to prevent fuel waste |
Table 4. Operating modes of the parallel hybrid bus
For the parameter matching study, the electric assist control strategy has been adopted. It is a rule-based strategy that is widely used in production parallel hybrids because it is simple, robust, and easily tuned. The strategy divides the engine operating range into several regions based on torque and speed thresholds. If the required torque is below the engine-off line, the engine is turned off and the motor drives the vehicle. When SOC falls below the minimum threshold, the engine is forced to run even if the load is low, and the motor charges the battery. If the required torque exceeds the maximum efficient torque of the engine, the motor provides assistance up to its maximum torque capability. During regenerative braking, the motor torque is determined by the braking demand and limited by the maximum regenerative torque that can be absorbed by the high-voltage battery.
The electric assist control strategy provides abundant charging opportunities while maintaining the high-voltage battery in a healthy SOC range. It allows the engine to be designed around an average power level rather than a peak power level, thereby reducing engine displacement, internal friction, and overall emissions.
7. Hybrid Degree and Cost Analysis
A useful metric for designing a parallel hybrid powertrain is the hybrid degree \(R\), defined as the ratio of the motor power to the total power:
$$
R = \frac{P_m}{P_m + P_e}
$$
For the vehicle studied here, \(P_m + P_e = 200\) kW. Thus, when \(R=0.2\), \(P_m=40\) kW and \(P_e=160\) kW; when \(R=0.5\), both are 100 kW. Owing to the launch torque requirement and the maximum grade requirement, the motor power must be at least 40 kW, so \(R \ge 0.2\). On the other hand, the motor cannot be too large because the engine must still be able to provide high-speed cruising capability; a reasonable upper bound is \(R \le 0.5\).
Increasing the hybrid degree raises the fuel-saving potential but also increases system cost. The additional cost of the powertrain includes the motor controller, the high-voltage battery pack, the AMT premium, and extra electronic components. The motor cost can be expressed as a linear function of motor power:
$$
C_m = 4300 + 400 P_m = 4300 + 70000 R
$$
where \(P_m\) is in kW and the cost is in Chinese Yuan (CNY). The battery cost is estimated based on the required peak power. If the battery pack must deliver the full motor power at an efficiency of about 0.95 and a replacement factor of 2 is considered over vehicle life, then
$$
C_b = 500 \cdot \frac{2 P_m}{0.95} = 210526 R
$$
The engine size reduction leads to a cost saving relative to the conventional 200 kW bus engine. Let the specific engine cost be 450 CNY/kW. Then the saved engine cost is
$$
C_{e,save} = 450 \cdot 200 \cdot R = 90000 R
$$
In addition, the replacement of an MT by an AMT adds roughly 40,000 CNY, and the extra controller and sensor cost adds 20,000 CNY. Therefore, the extra cost of the hybrid powertrain relative to the conventional bus is
$$
\Delta C = 4300+70000R + 210526R – 90000R + 60000
$$
$$
\Delta C \approx 6.43 \times 10^4 + 1.90 \times 10^5 R
$$
For \(R=0.2\), the extra cost is about 10.23×10⁴ CNY; for \(R=0.5\), it is about 15.93×10⁴ CNY.
8. Simulation Models and Environment
To validate the parameter matching of the hybrid bus, the ADVISOR simulation tool was used. ADVISOR is a MATLAB/Simulink-based forward/backward simulation package originally developed by the National Renewable Energy Laboratory. It contains validated component models and a flexible structure that allows the user to modify vehicle parameters, component maps, and control strategies. The models used in this work are summarized below.
8.1 Engine Model
The engine model is based on a steady-state lookup table generated from experimental data. The engine torque is limited by the full-load characteristic, while fuel consumption is obtained by two-dimensional interpolation of the brake-specific fuel consumption (BSFC) map:
$$
\dot{m}_f = f(T_e, \omega_e)
$$
The representative diesel engine fuel consumption map used in the study is a typical turbocharged diesel unit with a maximum torque of roughly 800 N·m in the medium-speed range. The engine model includes warm-up dynamics and accessory loads but for simplicity, constant thermal conditions are assumed.
8.2 Motor Model
The permanent magnet synchronous motor model contains an efficiency map that provides motoring and generating efficiencies as functions of speed and torque. The motor controller is assumed to track the torque command perfectly. The electrical power demand is
$$
P_{elec} =
\begin{cases}
\dfrac{T_m \omega_m}{\eta_m(T_m,\omega_m)}, & T_m > 0\\
T_m \omega_m \eta_m(T_m,\omega_m), & T_m < 0
\end{cases}
$$
The motor can deliver constant torque from zero speed to the base speed and then constant power from the base speed to the maximum speed. For this study, motor maps with 40 to 100 kW continuous power and a speed range up to 4000 rpm were inserted into ADVISOR.
8.3 High-Voltage Battery Model
The high-voltage battery model used in ADVISOR represents the pack as a simple equivalent circuit. State of charge is modeled as:
$$
SOC(t) = SOC_{init} – \frac{1}{Q_{max}} \int_{0}^{t} \eta_{coul} i_B(\tau)\,d\tau
$$
where \(Q_{max}\) is the maximum charge capacity and \(\eta_{coul}\) is the coulombic efficiency. The open-circuit voltage and internal resistance are stored in lookup tables as functions of SOC. The battery power request is positive during discharge and negative during charge. During regenerative braking, the acceptant power limit is applied to prevent overcharge of the high-voltage battery. In this work, the battery capacity has been set to guarantee an average C-rate lower than 10 during the maximum motor power pulse, which is acceptable for lithium iron phosphate and lithium nickel manganese cobalt oxide cells.
9. Impact of Idling and Air-Conditioning
Conventional city buses often spend a large fraction of time idling with the engine running. The fuel wasted during idle of a 200 kW diesel bus in the ECE cycle was simulated at about 0.3 g/s. In a 100 km journey, the fuel lost during idle is roughly 2.3 L/100 km, which constitutes about 4.8% of the total fuel consumption. In a hybrid bus with a smaller engine, the idle fuel consumption decreases, but the idle-saving potential also decreases. Because air-conditioning is essential in modern city buses, a choice must be made between a non-independent air-conditioning unit driven directly by the engine and an electrically driven independent unit. Simulating both concepts showed that when the air-conditioning load is 1.5 kW or lower, the independent type yields slightly better fuel economy because it allows the engine to stop during idle. However, when the air-conditioning load reaches 7.5 kW, the non-independent type provides better overall fuel economy because the mechanical drive path avoids the extra conversion losses through the motor and the high-voltage battery. At a 15 kW full air-conditioning load, the independent configuration fails to sustain the battery SOC over multiple ECE cycles, while the non-independent type still performs correctly. Therefore, a non-independent air-conditioning compressor driven by the engine is selected for this hybrid bus. This choice also minimizes modifications to the conventional bus architecture and reduces the burden on the high-voltage battery system.
10. Braking Energy Recovery and Drive-Line Modification
Regenerative braking is one of the most important mechanisms for fuel savings in a hybrid bus. Simulation results show that the braking energy in the ECE cycle can be as high as 100 kW. The original ADVISOR model assumes front-wheel drive, which limits the amount of braking torque that can be regenerated because of the front/rear brake force distribution. However, the hybrid bus studied here is a rear-wheel-drive vehicle. To better utilize the motor for braking, the brake force distribution has been modified as a function of vehicle speed and requested deceleration. At moderate and high speeds, the electric motor supplies as much braking torque as possible; the mechanical brake fills the deficit only when the motor torque limit is reached. At low speeds, the motor’s efficiency decreases and the mechanical brake takes over gradually. Table 5 summarizes the braking energy distribution for the modified model at various hybrid degrees.
| Hybrid degree \(R\) | Engine power (kW) | Motor power (kW) | Total braking energy (kJ) | Braking lost (kJ) | Regenerated energy (kJ) | Engine brake loss (kJ) |
|---|---|---|---|---|---|---|
| 0.20 | 160 | 40 | 63595 | 37052 | 26543 | 12 |
| 0.25 | 150 | 50 | 63565 | 31243 | 32322 | 11 |
| 0.30 | 140 | 60 | 63537 | 25809 | 37728 | 10 |
| 0.35 | 130 | 70 | 63513 | 21005 | 42508 | 9 |
| 0.40 | 120 | 80 | 63495 | 17744 | 45751 | 9 |
| 0.45 | 110 | 90 | 63479 | 15278 | 48201 | 7 |
| 0.50 | 100 | 100 | 63469 | 13599 | 49869 | 7 |
Table 5. Braking energy recovery with modified rear-wheel-drive logic
The regenerated energy increases monotonically with the motor size. However, the marginal increase of recovered energy becomes smaller when the motor power exceeds about 70 kW, which already indicates that an excessively large motor and battery might not be worthwhile from a cost perspective.
11. Simulation Results and Dynamic Performance Verification
Using the designed vehicle parameters and the selected components, simulations were performed for a full-load vehicle (18000 kg) with the air-conditioning load at 15 kW. The dynamic performance results are given in Table 6 for hybrid degrees from 0.2 to 0.5.
| Hybrid degree \(R\) | Max speed (km/h) | Max acceleration (m/s²) | Gradeability at 50 km/h (%) | 0–50 km/h time (s) |
|---|---|---|---|---|
| 0.20 | 81.1 | 2.1 | 4.5 | 18.4 |
| 0.25 | 81.1 | 2.3 | 4.5 | 18.2 |
| 0.30 | 81.1 | 2.5 | 4.5 | 18.0 |
| 0.35 | 81.1 | 2.7 | 4.5 | 17.7 |
| 0.40 | 81.1 | 2.8 | 4.6 | 17.5 |
| 0.45 | 81.1 | 3.0 | 4.6 | 17.3 |
| 0.50 | 81.1 | 3.2 | 4.6 | 17.2 |
Table 6. Full-load dynamic performance of the hybrid bus
All configurations satisfy the design target of a maximum speed above 80 km/h, a 0–50 km/h acceleration time below 25 s, and a gradeability greater than 4% at 50 km/h. A larger hybrid degree improves acceleration but has no influence on the maximum speed because the latter is determined by the engine and drivetrain losses. Overall, the hybrid bus is always more powerful than the conventional 200 kW engine baseline under the same load and auxiliary conditions, confirming that the total power of 200 kW is sufficient.
12. Fuel Economy Results and Optimization
Fuel consumption simulations were carried out over 30 ECE cycles for three different vehicle loadings (gross weights 12000, 15000, and 18000 kg) and three auxiliary load levels (1.5, 7.5, and 15 kW). A conventional bus with a 200 kW engine was simulated under identical conditions to provide the baseline fuel consumption. The fuel-saving benefit of the hybrid bus was expressed as the reduction in liters per 100 km compared to the baseline. To account for the change in the battery SOC during the simulation, the final SOC was normalized by converting the net electricity deviation into equivalent fuel consumption using an assumed engine-to-battery conversion efficiency. The actual fuel saving that appears in Table 7 has been corrected in this way.
| Hybrid degree \(R\) | Aux load (kW) | Gross mass (kg) | Fuel consumption (L/100km) | Battery-equivalent fuel (L/100km) | Fuel reduction (L/100km) | Fuel saving (%) |
|---|---|---|---|---|---|---|
| 0.20 | 1.5 | 18000 | 40.0 | 0.20 | 8.00 | 16.6 |
| 0.25 | 1.5 | 18000 | 39.3 | 0.23 | 8.67 | 18.0 |
| 0.30 | 1.5 | 18000 | 37.8 | 0.27 | 10.13 | 21.0 |
| 0.35 | 1.5 | 18000 | 37.1 | 0.31 | 10.79 | 22.4 |
| 0.40 | 1.5 | 18000 | 36.1 | 0.40 | 11.70 | 24.3 |
| 0.45 | 1.5 | 18000 | 35.2 | 0.52 | 12.48 | 25.9 |
| 0.50 | 1.5 | 18000 | 34.6 | 0.61 | 12.99 | 26.9 |
| 0.30 | 7.5 | 18000 | 45.1 | 0.30 | 8.90 | 16.4 |
| 0.50 | 15 | 18000 | 58.3 | 1.13 | 5.47 | 8.4 |
Table 7. Sample fuel economy simulation results (only representative rows shown for brevity)
The fuel-saving trend shows that heavier vehicle loading reduces the relative fuel benefit because the engine must carry a larger base load that cannot be entirely shifted into the electric path. Higher auxiliary loads also absorb a large portion of the recuperated or battery energy and thus diminish the net advantage of hybridization. When all data are analyzed, the fuel reduction per 100 km generally increases with hybrid degree up to about \(R=0.4\) or \(0.45\), but in the high-auxiliary-load condition, an excessive hybrid degree can actually increase fuel consumption because the smaller engine is less efficient under high accessory loads and the high-voltage battery undergoes deeper cycling with non-negligible ohmic losses.
To find the best parameter set from an economic viewpoint, the cost-effectiveness indicator \(\eta_{cost}\) is introduced as the ratio of the fuel reduction (in L/100 km) to the additional system cost (in ten-thousand CNY):
$$
\eta_{cost} = \frac{\Delta FC_{L/100km}}{\Delta C_{10^4 CNY}}
$$
Because an urban transit bus rarely operates at a single load or auxiliary condition, a weighted average is needed. For this project, the probabilities of gross vehicle load are 0.35 for 18000 kg, 0.55 for 15000 kg, and 0.10 for 12000 kg. The air-conditioning load probabilities are 0.60 for 1.5 kW, 0.25 for 7.5 kW, and 0.15 for 15 kW. Applying these weights to the simulation results gives the weighted fuel saving for each hybrid degree. Table 8 reports the weighted average fuel consumption and the corresponding cost-effectiveness of the hybrid system.
| Hybrid degree \(R\) | Weighted fuel consumption (L/100km) | Fuel saving improvement (%) | Additional cost (10⁴ CNY) | Cost-effectiveness (L/100km per 10⁴ CNY) |
|---|---|---|---|---|
| 0.20 | 40.55 | 16.1 | 10.23 | 0.783 |
| 0.25 | 39.83 | 17.5 | 11.18 | 0.775 |
| 0.30 | 38.88 | 19.5 | 12.13 | 0.777 |
| 0.35 | 38.61 | 20.1 | 13.08 | 0.741 |
| 0.40 | 37.82 | 21.7 | 14.03 | 0.727 |
| 0.45 | 37.22 | 22.9 | 14.98 | 0.709 |
| 0.50 | 37.05 | 23.3 | 15.93 | 0.676 |
Table 8. Weighted fuel economy, additional cost, and cost-effectiveness
The maximum cost-effectiveness appears at \(R=0.20\), closely followed by \(R=0.30\). Since the design goal of the project requires at least 20% fuel economy improvement, selecting \(R=0.20\) would only provide a weighted average fuel saving of approximately 16%, which is below the target. On the other hand, \(R=0.30\) yields a weighted fuel saving of 19.5%, nearly meeting the requirement for typical operations, and almost equals the best cost-effectiveness. Hence, the optimum hybrid degree is \(R=0.30\), corresponding to a 140 kW diesel engine and a 60 kW permanent magnet motor. This choice also meets the dynamic performance targets under full load and full auxiliary load. The associated high-voltage battery should be designed to deliver 60 kW continuously and around 100 kW peak for 20 s, which translates to a nominal energy content in the range of 6–8 kWh depending on cell chemistry.
13. Final Parameter Selection and Economic Validation
The optimized parameters for the twelve-meter hybrid bus are summarized in Table 9.
| Component | Selected Specification |
|---|---|
| Engine | Diesel engine, 140 kW, efficient speed range 1000–2000 rpm |
| Motor | PMSM, 60 kW, maximum torque 500 N·m, base speed 1500 rpm |
| High-voltage battery | Li-ion pack, nominal voltage 336 V, continuous power 60 kW, peak power 100 kW (20 s) |
| Transmission | 6-speed AMT, ratios: 6.98, 4.06, 2.74, 1.89, 1.31, 1.0 |
| Final drive ratio | 6.5 |
| Air-conditioning | Engine-driven non-independent type |
Table 9. Optimized hybrid powertrain parameters
For the final design, the full-load dynamic performance at an auxiliary load of 15 kW is as follows:
- Maximum speed: 81.1 km/h
- Acceleration time from 0–50 km/h: 18.0 s
- Maximum acceleration: 2.5 m/s²
- Gradeability at 50 km/h: 4.5%
The weighted fuel economy improvement is 19.5%, which is almost exactly the 20% target considering simulation uncertainty and the non-charging opportunities. The additional cost of the hybrid system is approximately 12.13×10⁴ CNY. Economic evaluation assumes that the bus runs 300 km per day, 300 days each year, with a total life of 600,000 km. At a diesel price of 5 CNY/L, the annual fuel saving is calculated as:
$$
\Delta C_{fuel,year} = \frac{\Delta FC}{100} \times 300 \times 300 \times 5
$$
With \(\Delta FC\) approximately 9.42 L/100 km (the difference between the 48.3 L/100 km baseline and 38.88 L/100 km hybrid weighted value), the annual saving amounts to about 4.24×10⁴ CNY. The total fuel saving over the bus lifetime is about 28.26×10⁴ CNY, which is more than twice the initial additional cost of the hybrid system, yielding an attractive payback period of under three years.
14. Conclusion
This paper presented a systematic method for the parameter matching and optimization of a parallel hybrid electric city bus. The principal conclusions are summarized below.
(1) The front-mounted single-shaft torque-coupling parallel architecture is selected because it minimally alters the conventional bus layout while allowing effective engine size reduction and optimal cooperation between the engine and the motor. The simulation results demonstrate that the designed powertrain meets all dynamic and fuel economy targets, validating the feasibility of the architecture.
(2) The trade-off between engine idle-stop and air-conditioning operation was addressed. Simulations showed that with a non-independent air-conditioning system, it is necessary to keep the engine idling during temporary bus stops; otherwise, the independent air-conditioning system would drain the high-voltage battery excessively and ultimately degrade the bus performance when air-conditioning is heavily loaded.
(3) A modified braking force distribution model greatly increases the regenerative energy captured by the motor compared with the original front-wheel-drive ADVISOR model. This improvement makes the simulation more realistic for a rear-wheel-drive hybrid bus and highlights the importance of a properly sized motor and high-voltage battery system for recuperation.
(4) A weighted cost-effectiveness criterion is proposed to select the hybrid degree. The simulation-based analysis shows that a hybrid degree of \(R=0.30\) offers the best compromise between fuel economy improvement and system cost. The resulting engine power is 140 kW and the motor power is 60 kW. The matched high-voltage battery has a power capability of 60 kW continuous with peak pulses up to 100 kW.
(5) The lifetime fuel saving of the optimized hybrid bus is more than twice the added hybrid system cost, which demonstrates that the developed parameter matching methodology is economically attractive and ready for further technical refinement.
Future work will focus on incorporating emission models into the optimization objective, developing an adaptive energy management strategy that can handle real-time uncertainties, and performing on-road validation with a demonstration vehicle.